Right isosceles triangle

Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?

Result

S =  25 cm²

Solution:

$c_{ 1 } = 5 \ cm \ \\ c_{ 2 } = c_{ 1 } = 5 = 5 \ cm \ \\ c = c_{ 1 }+c_{ 2 } = 5+5 = 10 \ cm \ \\ \ \\ h = \sqrt{ c_{ 1 } \cdot \ c_{ 2 } } = \sqrt{ 5 \cdot \ 5 } = 5 \ cm \ \\ \ \\ S = \dfrac{ c \cdot \ h }{ 2 } = \dfrac{ 10 \cdot \ 5 }{ 2 } = 25 = 25 \ cm^2$

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